Lockbox system Eagle Industries feels that a lockbox system can shorten its accounts receivable collection period by $4$ days. Credit sales are $$2,500,000$ per year, billed on a continuous basis. The firm has other equally risky investments with a return of $16\%.$ The cost of the lockbox system is $$11,000$ per year. $($Note: Assume a $365-$day year.$)$

a$.$ What amount of cash will be made available for other uses under the lockbox system?

b$.$ What net benefit $($cost$)$ will the firm realize if it adopts the lockbox system? Should it adopt the proposed lockbox system?

a$.$ The amount of cash that will be made available for other uses under the lockbox system is $ $q,($Round to the nearest dollar.$)$